Think straight or think again? Continual joint learning of deduction, abduction and induction

Deduction, abduction and induction are the three primary forms of logical reasoning. Although they complement each other, they are typically studied separately. In this paper, we investigate their roles in a unified paradigm and propose a continual joint reasoning framework. According to the cognitive theory, the three reasoning methods could be combined in a dynamic cycle. We thus design a three-level learning procedure. First, deduction and abduction are formulated as generation tasks and connected via dual learning to validate each other for mutual improvements. Second, we introduce induction as a fact retriever to support and guide the above dual learning. Finally, to alleviate the data scarcity issue, we design a policy gradient method to allow continuous enhancements based on inferred pseudo training data, instead of expensive parallel annotations. In particular, we design three types of rewards to estimate the quality of the inferred pseudo training data and to avoid the model collapse issue. Extensive experiments, including human evaluation, reveal their mutual effects and verify the synergy effects of the three forms of logical reasoning. Notably, our GPT-2-based framework can achieve comparable performance with GPT-3.5 in human evaluation.